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Equation 2 provides for calculation of NDVI* as proposed by Gillies et al. (1997). The <br />parameters NDVIo and NDVIs were determined using the methods presented in Baugh <br />and Groeneveld (2006), described below. These two parameters stretch the NDVI* <br />distribution from 0 to 1. <br />NDVI*; _ NDVI, - NDVIo i ~NDVIs - NDVIo (z) <br />Where "i" denotes the ith pixel <br />NDVIo =NDVI at zero vegetation cover <br />NDVIs =NDVI at peak vegetation (saturation) <br />Figure 1 presents a graphic view of an example cumulative distribution function (CDF) <br />of NDVI in which NDVIo is predicted using linear regression. After subtraction, the <br />lower tail of the curve below NDVIo, yields a small set of negative values that were set to <br />zero to avoid creating negative values for ET. Very low values of NDVI, often less than <br />zero, also generally occur for clear open water in most TM scenes and scene subsets. <br />These water values, also set to zero, are of interest for quantification of surface <br />evaporation (E) and were identified and quantified in a separate step using a different <br />method employing a different TM channel, Band 5. <br />CDF -August 8, 1986 - <br />Data from San Luis Valley, Colorado <br />3500 <br />~ > <br />~ 3000 y = 25023x - 3736.5 ~ <br />v 250a <br />200o y' <br />a <br />1500 <br />1000 r <br />~ 500 x intercept = Q.1436 <br />U ~- <br />a <br />0 0.1 0.2 0.3 0.4 0.5 <br />NDVI <br />Figure 1. <br />An example CDF of NDVI <br />for data from San Luis <br />Valley, Colorado. NDVIo was <br />predicted using linear <br />regression (x-intercept) of <br />the lowest linear portion of <br />the CDF. The intercept <br />value is equivalent to NDVIo <br />in Equation 2. <br />Figure 2 presents examples of CDFs as raw NDVI (Figure 2a), and after application of <br />Equation 2 as NDVI* (Figure 2b). As can be seen in these graphs, the variation in NDVI <br />before calculation of NDVI* can be extreme; calculation of NDVI* enables viewing an <br />orderly progression of CDFs. Baugh and Groeneveld (2006) showed that the orderly <br />progression of NDVI* represented a significant enhancement of the signal for vegetation <br />response to antecedent precipitation. <br />As has been determined in numerous studies within the literature, NDVI is a competent <br />indicator of leaf area, photosynthesis and water use by vegetation. NDVI* is a further <br />refinement that removes non-systematic scatter and improves the hydrologic signal. In <br />4 <br />